We report the results of our intensive intranight optical monitoring of 8 `radio-intermediate quasars (RIQs) having flat or inverted radio spectra. The monitoring was carried out in {it R-} band on 25 nights during 2005-09. An intranight optical variability (INOV) detection threshold of $sim$ 1--2% was achieved for the densely sampled differential light curves (DLCs). These observations amount to a large increase over those reported hitherto for this rare and sparsely studied class of quasars which can, however, play an important role in understanding the link between the dominant varieties of powerful AGN, namely the radio-quiet quasars (RQQs), radio-loud quasars (RLQs) and blazars. Despite the probable presence of relativistically boosted nuclear jets, clear evidence for INOV in our extensive observations was detected only on one night. These results demonstrate that as a class, RIQs are much less extreme in nuclear activity compared to blazars. The availability in the literature of INOV data for another 2 RIQs conforming to our selection criteria allowed us to enlarge the sample to 10 RIQs (monitored on a total of 42 nights for a minimum duration of $sim 4$ hours per night). The absence of large amplitude INOV $(psi > 3%)$ persists in this enlarged sample. This extensive database has enabled us to arrive at the first estimate for the INOV Duty Cycle (DC) of RIQs. The DC is found to be small ($sim$ 9%). The corresponding value is known to be $sim 60%$ for BL Lacs and $approx 15%$ for RLQs and RQQs. On longer-term, the RIQs are found to be fairly variable with typical amplitudes of $approx$ 0.1-mag. The light curves of these RIQs are briefly discussed in the context of a theoretical framework proposed earlier for linking this rare kind of quasars to the much better studied dominant classes of quasars.
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